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3 Answers
3

Matt pretty much gave the answer, but I'm going to be cheeky and write a real answer, since I think the question deserves it.

This ん is not the negative, but a contraction of the archaic auxiliary verb む, which expresses intention, prediction etc. As the Goo article says, since the Heian period, it also appeared as ん, and since the Kamakura period as (よ)う. The latter is basically the modern Japanese volitional verb suffix.

I cannot think of any situation where the む form survives in modern Japanese. The ん form survives in certain fossilized constructs:

生きんがため in order to live
言わんとする intend to say

Incidentally, these could also be expressed with the (よ)う form:

生きようがため in order to live
言おうとする intend to say

Edit:

In terms of meaning, there is not much of a difference, but the んがため・んとする versions sound a bit more old-fashioned/solemn. So the difference in use is mostly stylistic.

I would like to propose this alternate translation, though I don't completely grasp the Japanese : My Grandfather takes great care to mind his diet in order to live until 100yrs of age. (in the original Japanese, is the meaning that he has already reached 100years of age? or is he trying to each 100 years of age?)
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yadokariMay 1 '12 at 18:29

Presumably, the correct answer is B. Even if B is derived from A, that form isn't used. (Possibly because it invokes the archaic sense of ぬ noted in the Wictionary? This could be a case of the vestiges of something archaic which survives in an altered form only.)

Unfortunately, this etymology is not correct. The source of the ん here is not ぬ but む, which you can think of as the ancestor to the modern -(y)ou verb ending. That's why it's 勝たんがために and not 勝ちんがために, for example.
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MattMay 2 '12 at 0:45

Aha, I seem to remember one of the answers I pointed to in that discussion discusses む versus ぬ. I will go back to that and read it in detail.
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KazMay 2 '12 at 1:31